# Beta is symmetric

The following formula holds: $$B(x,y)=B(y,x),$$ where $B$ denotes the beta function.
Using beta in terms of gamma, we may calculate $$B(x,y)=\dfrac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)} = \dfrac{\Gamma(y)\Gamma(x)}{\Gamma(y+x)} = B(y,x),$$ as was to be shown.